Taken together, these points remove the need for coordinated search of the joint policy space \(\mathbf {\Pi }\) : since \((\mathcal {V}^{*}, \mathcal {W}^{*})\) -subjective \(\epsilon \) -satisficing paths to equilibrium exist within \(\mathbf {\Pi }\)  and \(\mathbf {\Pi }\)  is finite, play can be driven to \(\epsilon \) -equilibrium even by random policy updating by those players that are not subjectively \(\epsilon \) -best-responding. Moreover, this structure also removes the need for specialized policy updating rules (such as inertial best-responding [1]} or gradient ascent [2]}) that taken into account special structure in the game.
